We have shown how the cooking problem can be solved by a series
of reductions and conventions. Binding allows the reduction of the
problem to a schematic world in which action is greatly restricted and
so action selection is greatly simplified. This world can be further
reduced, given algorithms for resetting tools, to a world in which
tools are always reset. This world, in turn, is equivalent to a world
in which there is only one object, the material being cooked, and only
one action can be taken at any given time. Such actions can be found
by table lookup.

Multiple materials can be cooked by interleaving the execution of
processes for cooking the individual materials. Interleaving the
processes is equivalent, however, to interleaving the bindings, so the
schematic-world algorithm need not even be aware that it is pursuing
multiple goals. If tool bindings are continuously changed as tools
are dirtied then tools are effectively disposable, tools effectively
have only a single state, and the separate reduction from general
tools to single-state tools is unnecessary. Material bindings can be
maintained by any number of conventions involving the states and/or
positions of objects.

In short, we can describe a TOAST algorithm as a path through a
network of possible simplifications of the problem (see Figure
6) in which every path from the actual world to
the idealized single-object world defines a possible (and correct)
version of the TOAST algorithm.